Question: Solve for $x$ and $y$ using elimination. ${6x-y = 26}$ ${-5x+y = -20}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {6x-y = 26}\thinspace$ to find $y$ ${6}{(6)}{ - y = 26}$ $36-y = 26$ $36{-36} - y = 26{-36}$ $-y = -10$ $\dfrac{-y}{{-1}} = \dfrac{-10}{{-1}}$ ${y = 10}$ You can also plug ${x = 6}$ into $\thinspace {-5x+y = -20}\thinspace$ and get the same answer for $y$ : ${-5}{(6)}{ + y = -20}$ ${y = 10}$